Marginal Rate Of Substitution Research Articles

A formula for the elasticity of substitution of a large class of smooth utility functions

We derive a general formula for the elasticity of substitution of a large class of smooth utility functions. This formula depends critically on two terms: the marginal rate of substitution and the elasticity of marginal utility, which may be interpreted according to the context either as the coefficient of relative risk aversion or as the intertemporal elasticity of substitution. This formula works for homothetic and non-homothetic utility functions. Besides, it holds for two important class utility functions often used in both empirical and theoretical works: the quasi-linear utility and the Stone-Geary utility functions.

On the properties of the labour wedge: hours worked and government transfers in perspective

ABSTRACT Questions surrounding the labour wedge and the tax wedge in the United States are complicated by the fact that, historically, there is a lack of coherent relationship between the series of hours worked (based on standard measurements) and that of the tax wedge. This has been cited as grounds for discounting the tax wedge as a viable explanation for the behaviour of the labour wedge. In this paper, I explore an alternative measurement of labour hours in the United States in a bid to clear up some of the morass surrounding the tax wedge and hours worked. In the process, I show that, the labour wedge is rather more aligned with available labour hours over the business cycle than it does actual hours worked. Moreover, cyclical properties of the available hours series, however puzzling, are explained by the presence of a government transfer scheme which I introduce in the household side of the market. Also, the presence of the transfer scheme alters the marginal rate of substitution (MRS) between consumption and leisure, and by doing so, reverses the cyclical properties of the tax wedge. This puts the tax wedge in alignment with the labour wedge over the business cycle.

Physician altruism under the change from pure payment system to mixed payment schemes: experimental evidence

BackgroundMixed payment schemes have become one of the effective measures to balance medical costs and quality of medical services. However, altruism as an intrinsic motivation may influence the effect of switching from a pure payment system to mixed payment schemes. This study aimed to quantify physicians’ altruism and analyze the effect of changes of payment system on physicians’ altruism and thus proposed references for the reform of payment system.MethodsWe simulated an exogenous payment system in a controlled laboratory with five experimental groups and 150 medical student subjects. Physicians’ altruism was measured by estimating altruistic parameter and marginal rate of substitution. The non-parametric test and the least square regression analysis were used to analyze the differences of altruistic parameters between pure payment systems and mixed payment schemes. Finally, we analyzed the effect of changes in payment system accompanied by changes in trade-off range on physicians’ altruism.ResultsWe find that the mean value of individual altruistic parameter is 0.78 and the marginal rate of substitution is 1.078. Their estimates at the individual level were significantly positively correlated (Spearman’s ρ = 0.715, p < 0.01). The shift from pure payment system to mixed payment scheme reduced the altruistic parameter. However, the altruistic parameter increased with the increase of the trade-off range. Physicians who were more altruistic generated higher patients’ health benefit. For each unit increase in altruistic parameter, the increase in patients’ health benefit was lower in mixed payment scheme than in the pure payment system.ConclusionThe estimates of altruistic parameters are reliable. Physicians attach a higher weight to patients’ benefit than to their own profit. Mixed payment schemes improve physicians’ behavior and relate to lower altruistic parameters; physicians only need to sacrifice less personal profits to generate the same or even higher altruistic parameter as under the pure payment system. The design of mixed payment schemes that make the interests of physicians and patients close to each other by reducing the trade-off range can provide implication for the reform of payment system in which the physicians’ interest and the patients’ benefit are consistent.

Patient preferences do matter: a discrete choice experiment conducted with breast cancer patients in six European countries, with latent class analysis.

The evolution of breast cancer (BC) treatments has resulted in tailored therapies for the different types and stages of BC. Each treatment has a profile of benefits and adverse effects which are taken into consideration when planning a treatment pathway. This study examines whether patients' preferences are in line with what is considered important from decision makers viewpoint. An online discrete choice experiment was conducted in six European countries (France, Germany, Ireland, Poland, Spain, UK) with BC patients. Six attributes were included: overall survival (OS), hyperglycemia, rash, pain, functional well-being (FWB), and out-of-pocket payment (OOP). Sixteen choice sets with two hypothetical treatments and a "No treatment" option were presented. Data were analyzed with the use of heteroscedastic conditional, mixed logistic, and latent class models. Marginal rate of substitution (MRS) were estimated for OOP versus the rest of attributes to establish the ranking of preferences for each attribute. Two hundred and forty-seven patients with advanced or metastatic BC and 314 with early-stage BC responded. Forty-nine percent of patients were<44 years old and 65 percent had completed university education. The MRS of the analysis demonstrated that "severe pain" is the highest dis-preferred attribute level, followed by "severe impairment in FWB" and OS. Four classes of patients as "decision makers" were identified. This study suggests that there is heterogeneity in treatment preferences of BC patients depending on their sociodemographic and disease-related characteristics. In combination with clinical guidelines, patient preferences can support the selection and tailoring of treatment options.

The Generalized Risk-Adjusted Cost-Effectiveness (GRACE) Model for Measuring the Value of Gains in Health: An Exact Formulation

AbstractThe generalized risk-adjusted cost-effectiveness (GRACE) analysis method modifies standard cost-effectiveness analysis (CEA), the primary method currently used worldwide to value health improvements arising from healthcare interventions. Generalizing standard CEA, GRACE allows for decreasing or even increasing returns to health. Previous presentations of GRACE have relied extensively on Taylor Series expansion methods to specify key model parameters, including those that properly adjust for illness severity and preexisting disability, consequences of uncertain treatment outcomes, and the marginal rate of substitution between life expectancy and health-related quality of life. Standard CEA cannot account for these sources of value or cost in its valuation of medical treatments. However, calculations of GRACE measures based on Taylor Series are approximations, which may be poorly behaved in some contexts. This paper provides a new approach for implementing GRACE, using exact utility functions instead of Taylor Series approximations. While any proper utility function will suffice, we illustrate with three well-known functions: constant relative risk aversion (CRRA) utility; hyperbolic absolute risk aversion (HARA) utility, of which CRRA is a special case; and expo-power (EP) utility, of which constant absolute risk aversion (CARA) is a special case. The analysis then extends from two-period to multiperiod models. We discuss methods to estimate parameters of HARA and EP functions using two different types of data, one from discrete choice experiments and the other from “happiness economics” methods. We conclude with some reflections on how this analysis might affect benefit-cost analysis studies of healthcare interventions.

Monetary Policy, Neutrality, and the Environment

AbstractWe study the interaction between monetary/fiscal policies in a Ramsey–Sidrauski model augmented with the “Green Golden Rule.” We demonstrate conditions whereby monetary and fiscal policy under different utility and preference assumptions are or are not environmentally neutral. Despite its nonseparability in utility, we demonstrate that money is environmentally neutral. Policy impacts the environment via the marginal rate of transformation rather than the marginal rate of substitution between consumption and environment. Fiscal policies under a balanced budget are environmentally nonneutral. Only under a nonbalanced budget, when deficits are monetized, is money environmentally nonneutral. Under cash‐in‐advance and transactions costs, money is environmentally nonneutral.

Consumption Pattern Benefits of the Cultural Activities in South Korea

This study examines the relationship between the cultural consumption pattern and an individual’s subjective well-being. We divide the consumption pattern of cultural activities by frequency, diversity, and inclusion and estimate the monetary value of the participation in culture and arts activities through the marginal rate of substitution. To reduce omitted variable bias, various factors are controlled for, such as basic demographics and satisfaction with personal relationship, class awareness, subjective income level, charitable donations and voluntary activities. The results show that the consumption of cultural activities can improve the individual’s subjective well-being, thus suggesting the use of cultural vouchers. Specifically, we find that the coefficients on frequency are positive and statistically significant, indicating that the cultural activities in Korea have a positive relationship with an individuals’ subjective well-being. Our research provides insight to the government organizations involved in the promotion of leisure policies.

A Comparison of Ordered Categorical versus Discrete Choices within a Stated Preference Survey of Whole-Blood Donors.

This article compares the relative preferences from stated preference (SP) questions requiring ordered categorical versus discrete choice responses. The approaches were contrasted for blood donation service characteristics that offer opportunities to donate blood.The estimates of relative preferences for alternative blood donation service characteristics were similar between the 2 forms of SP approach.This study illustrates how SP survey questions can be formulated to provide responses on an ordered categorical scale and to estimate marginal rates of substitution between different attributes, which can be compared with those derived from discrete choice experiment (DCE) choices.The article highlights the potential value of considering alternative choice framings rather than relying solely on DCEs.

Consumers’ preference for urban last-mile delivery: effects of value perception and long-term COVID-initiated contextual shifts

ABSTRACT The economic and environmental challenges associated with Last Mile Delivery (LMD) give rise to the self-collection concept, yet the practical adoption is often below expectations. In this consumer-centric segment, adequate understandings of consumers are vital but are often lacking. To address this gap, this study examines consumers’ LMD preference with the Integrated Choice and Latent Variable framework. A stated choice experiment was commissioned in Singapore during the transition of COVID pandemic toward endemic. Our results showed that consumers accept unattended delivery methods and are no longer concerned with the delivery time window, a traditionally critical delivery attribute. Regarding latent perceptions, this study confirmed the significant effects of value perception on self-collection preferences. Nonetheless, individuals’ environmental consciousness was found to be insignificant. The relative effects of specific value statements were quantified using the marginal rate of substitution and the mediation roles of value perception on the sociodemographic-preferences relationships were validated.

Trade-offs during the COVID-19 pandemic: A discrete choice experiment about policy preferences in Portugal.

The need to control the sanitary situation during the COVID-19 pandemic has led governments to implement several restrictions with substantial social and economic impacts. We explored people's trade-offs in terms of their income, life restrictions, education, and poverty in the society, compared to their willingness to avoid deaths. We applied a web-based discrete choice experiment to elicit preferences of the Portuguese citizens for these attributes and computed the marginal rate of substitution in terms of avoided deaths. We recorded 2,191 responses that faced the possibility of having 250 COVID-19 related deaths per day as the worst possible outcome from the choice levels presented. Estimates suggested that individuals would be willing to sacrifice 30% instead of 10% of their income to avoid approximately 47 deaths per day during the first six months of 2021. For the same period, they would also accept 30% of the students' population to become educationally impaired, instead of 10%, to avoid approximately 25 deaths; a strict lockdown, instead of mild life restrictions, to avoid approximately 24 deaths; and 45% of the population to be in risk of poverty, instead of 25%, to avoid approximately 101 deaths. Our paper shows that avoiding deaths was strongly preferred to the remaining societal impacts; and that being a female, as well as working on site, led individuals to be more averse to such health hazards. Furthermore, we show how a DCE can be used to assess the societal support to decision-making during times of crisis.

OP03 Patient Characteristics Affect Their Treatment Choice: A Discrete Choice Experiment With Breast Cancer Patients In Six European Countries

IntroductionThe evolution of breast cancer treatments over the last decade has resulted in tailored therapies for the different types and stages of breast cancer. Each treatment has a profile of benefits and adverse effects which are taken into consideration when planning a treatment pathway. The objective of this study is to examine whether patients’ preferences are in line with what is considered important from policy-makers viewpoint.MethodsAn online discrete choice experiment (DCE) was conducted in six European countries (France, Germany, Ireland, Poland, Spain, UK) with breast cancer (BC) patients. The DCE comprised of six attributes: overall survival (OS), hyperglycaemia, rash, pain, functional well-being (FWB) and out-of-pocket payment (OOP). Sixteen choice sets with two hypothetical treatments and a “no treatment” option were presented. Sociodemographic and disease related data were collected. Heteroscedastic conditional and mixed logistic models accounted for scale and preference heterogeneity between countries and patients respectively. Latent class analysis categorized patients in classes. Marginal rates of substitution (MRS) were estimated for OOP versus the rest of attributes to establish the ranking of preferences for each attribute.ResultsTwo hundred and forty-seven patients with advanced or metastatic BC and 314 with early-stage BC responded. Forty-nine percent of patients were less than 44 years old and 65 percent had completed university education. The MRS of the analysis demonstrated that “severe pain” is the highest dis-preferred attribute level, followed by “severe impairment in FWB” and OS. Four classes of patients as “decision-makers” were identified. Additionally, there is sensitivity in preferences for both levels of pain and FWB depending on the stage of the disease.ConclusionsThis study suggests that there is heterogeneity in treatment preferences of breast cancer patients depending on their sociodemographic and disease related characteristics. In combination with clinical guidelines, patient preferences can support the selection and tailoring of treatment options.

Is survival a luxury good? Income elasticity of the value per statistical life

The value of a change in mortality risk is conventionally described by the marginal rate of substitution between income and mortality risk–the value per statistical life (VSL). The income elasticity of VSL is important for estimating how the value of mortality risk varies with time (for evaluating programs with long-lived effects) and across populations with different income levels (for evaluating programs with international consequences). Previous estimates of income elasticity based on meta-analysis of wage-differential studies and cross-sectional comparisons in stated-preference studies suggest values between about one-half and one. We present new estimates based on a 16-year series of wage-differential estimates in Taiwan. Between 1982 and 1997, estimated VSL increased by a factor of five while household labor earnings increased by 60 percent, per capita GDP increased two-and-a-half fold, and the occupational fatality rate in manufacturing and service industries decreased by half. Comparing the growth of VSL with that of household income implies the income elasticity is between about two and five, but this estimate may be biased by the endogeneity of VSL, which is affected by workers’ job choices. Using a two-stage approach to control for endogeneity yields estimates of the income elasticity of VSL between two-thirds and one, consistent with estimates from other approaches.

The moment restrictions for the durable consumption model with recursive utility revisited

A key assumption behind the moment restrictions for the durable consumption model with recursive utility is that a condition called normalization holds for the intertemporal marginal rate of substitution. This paper points out that one of the moment restrictions used in the literature is inconsistent with the assumption that this condition and the first-order conditions hold simultaneously. It shows that a two-step estimation procedure can avoid this issue. The method is illustrated with US data.

Understanding what matters to metastatic castration-resistant prostate cancer (mCRPC) patients when considering treatment options: A US patient preference survey.

Understanding how patients perceive the efficacy, safety, and administrative burden of treatments for metastatic castration-resistant prostate cancer (mCRPC) can facilitate shared-decision making for optimal management. This study sought to elicit patient preferences for mCRPC treatments in the US. We conducted a cross-sectional survey using the discrete-choice experiment method. Participants were asked to state their choices over successive sets of treatment alternatives, defined by varying levels of treatment attributes: overall survival (OS), months until patients develop a fracture or bone metastasis, likelihood of requiring radiation to control bone pain, fatigue, nausea, and administration (i.e., oral/IV injection/IV infusion). Using mixed logit models, we determined the value (i.e., preference weights) that respondents placed on each attribute. Relative attribute importance (RAI) and marginal rates of substitution (MRS) were calculated to understand patients' willingness to make tradeoffs among different attributes. The final data set numbered 160 participants, with a mean age of 71.6 years old and a mean of 8.96 years since prostate cancer diagnosis. Participants' treatment preferences were as follows: OS (RAI: 31%), bone pain control (23%), nausea (16%), delaying fracture or bone metastasis (15%), fatigue (11%), and administration (3%). The MRS demonstrated that respondents were willing to trade 1.9months of OS to eliminate moderate nausea and 3.3months of OS for a reduction in fatigue from severe to mild. Improving OS is the highest priority for patients with mCRPC, but they are willing to trade some survival to reduce the risk of requiring radiation to control bone pain, delay a fracture or bone metastasis, and experience less severe nausea and fatigue.

Measuring Preferences for Income Equality and Income Mobility

Abstract This paper quantifies preferences for income equality and mobility by generating statistics that are uncorrelated with beliefs and can be interpreted as marginal rates of substitution (MRS). All else constant, U.S. residents are willing to reduce average income by $2,744 to reduce the 90/10 income inequality ratio one unit and $1,228 to increase income mobility from the bottom quintile one percentage point. Democrats and Independents have similar preferences for both social variables, while Republicans have an MRS that is about two-thirds of Democrats and Independents for both income inequality and mobility.

Do patients’ preferences prevail in hospital selection?: a comparison between discrete choice experiments and revealed hospital choice

BackgroundIn patient choice, patients are expected to select the provider that best fits their preferences. In this study, we assess to what extent the hospital choice of patients in practice corresponds with their preferred choice.MethodsDutch patients with breast cancer (n = 631) and cataract (n = 1109) were recruited. We employed a discrete choice experiment (DCE) per condition to measure stated preferences and predict the distribution of patients across four hospitals. Each DCE included five attributes: patient experiences, a clinical outcome indicator, waiting time, travel distance and whether the hospital had been recommended (e.g., by the General Practitioner (GP)). Revealed choices were derived from claims data.ResultsHospital quality was valued as most important in the DCE; the largest marginal rates of substitution (willingness to wait) were observed for the clinical outcome indicator (breast cancer: 38.6 days (95% confidence interval (95%CI): 32.9–44.2); cataract: 210.5 days (95%CI: 140.8–280.2)). In practice, it was of lesser importance. In revealed choices, travel distance became the most important attribute; it accounted for 85.5% (breast cancer) and 95.5% (cataract) of the log-likelihood. The predicted distribution of patients differed from that observed in practice in terms of absolute value and, for breast cancer, also in relative order. Similar results were observed in population weighted analyses.DiscussionStudy findings show that patients highly valued quality information in the choice for a hospital. However, in practice these preferences did not prevail. Our findings suggest that GPs played a major role and that patients mostly ended up selecting the nearest hospital.

Incarceration risk, asset pricing, and black‐white wealth inequality

AbstractIntroductionHistorically, black Americans have been disproportionately at the bottom quantiles of the wealth distribution. As the choice of making any investment that can increase future wealth requires equating an asset's price to its return adjusted by a stochastic discount factor, this article considers if black‐white differences in the risk of incarceration, which can reduce the intertemporal marginal rate of substitution in consumption, matters for black‐white differences in wealth.MethodsWith repeated cross‐section data from the U.S. General Social Survey, we estimate the parameters of ordinal regression treatment specifications of individual wealth levels to measure the effects of incarceration risk on wealth.ResultsParameter estimates reveal that individual wealth levels vary inversely with incarceration risk. As black Americans have relatively higher incarceration risks, this suggests that at least part of the black‐white wealth gap can be explained by racial differences in incarceration risk.ConclusionCriminal justice reforms that reduce black‐white disparities in incarceration rates could also reduce black‐white disparities in wealth.

Effects of changes in preferences in moral hazard problems

This study examines the effects of changes in an agent's preferences over income and effort on the principal's costs. The incentive cost is fundamentally affected by two factors: the income-effort marginal rate of substitution at the first-best wage, and the degree of absolute risk aversion around it. Thus, a resulting increase in the first-best wage has mixed effects because both factors are altered simultaneously. When the limited liability constraint does not bind and if the utility is concave with respect to the inverse of the marginal utility, a decrease in the marginal rate of substitution, an increase in the degree of risk aversion, and an increase in the first-best wage will raise both incentive and agency costs. However, when the constraint binds and if the marginal rate of substitution at the minimum payment decreases, an increase in the degree of risk aversion and an increase in the first-best wage will raise agency cost. Even if the first-order approach is not valid, the results still hold under the log-submodularity of the marginal cost.

Valuing the impact of self-rated health and instrumental support on life satisfaction among the chinese population

BackgroundResearch has highlighted that satisfaction in health, and instrumental support (IS) are key areas of life affecting an individual’s wellbeing. Many social and public health initiatives use these two intervention mechanisms to improve individual’s wellbeing. For the purpose of cost-benefit assessment, there has been growing interest in expressing these intervention effects in economic terms. However, only a handful of studies have ever estimated these effects in economic terms, none of which examined them in a Chinese context. The aim of this study is to extend this line of valuation work to the Chinese population, estimating the implicit willingness-to-pays on the effects of improving individuals’ self-rated health (SRH) status and IS on their life satisfaction (LS).MethodsUsing data from a two-wave representative panel survey in Hong Kong (n = 1,109), this study conducted a cross-lagged analysis with a structural equation modelling technique to examine the causal effects of SRH and IS on LS. The use of this cross-lagged approach was an effort to minimise the endogeneity problem. Then, substituting the respective estimates to the formulae of compensating surplus, the marginal rate of substitution of SRH and IS with respect to individual’s equivalised monthly household income (HI) were estimated and were then expressed as the implicit willingness-to-pays on the effect of improving individuals’ SRH and IS on their LS.ResultsThe cross-lagged analysis ascertained the causal effects of SRH (β = 0.074, 95% Confidence Interval: 0.021, 0.127) and IS (β = 0.107, 95% Confidence Interval: 0.042, 0.171) on individuals’ satisfaction with life. Translating into the concept of compensating surplus, the implicit monetary values of improving the sample’s SRH from “poor health” to “excellent health” and their perceived IS from “little support” to “a lot of support” are equivalent to an increase in their equivalised monthly HI by US$1,536 and US$1,523 respectively.ConclusionsThis study is the first to derive the implicit monetary values of SRH and IS on individual’s LS in a predominantly Chinese society, and it has implications for the cost-benefit assessment in wellbeing initiatives within the population.

The FACT-8D, a new cancer-specific utility algorithm based on the Functional Assessment of Cancer Therapies-General (FACT-G): a Canadian valuation study

IntroductionUtility instruments are used to assess patients’ health-related quality of life for cost-utility analysis (CUA). However, for cancer patients, the dimensions of generic utility instruments may not capture all the information relevant to the impact of cancer. Cancer-specific utilities provide a useful alternative. Under the auspices of the Multi-Attribute Utility in Cancer Consortium, a cancer-specific utility algorithm was derived from the FACT-G. The new FACT-8D contains eight dimensions: pain, fatigue, nausea, sleep, work, support from family/friends, sadness, and worry health will get worse. The aim of the study was to obtain a Canadian value set for the FACT-8D.MethodsA discrete choice experiment was administered to a Canadian general population online panel, quota sampled by age, sex, and province/territory of residence. Respondents provided responses to 16 choice sets. Each choice set consisted of two health states described by the FACT-8D dimensions plus an attribute representing survival duration. Sample weights were applied and the responses were analyzed using conditional logistic regression, parameterized to fit the quality-adjusted life year framework. The results were converted into utility weights by evaluating the marginal rate of substitution between each level of each FACT-8D dimension with respect to duration.Results2228 individuals were recruited. The analysis dataset included n = 1582 individuals, who completed at least one choice set; of which, n = 1501 completed all choice sets. After constraining to ensure monotonicity in the utility function, the largest decrements were for the highest levels of pain (− 0.38), nausea (− 0.30), and problems doing work (− 0.23). The decrements of the remaining dimensions ranged from − 0.08 to − 0.18 for their highest levels. The utility of the worst possible health state was defined as − 0.65, considerably worse than dead.ConclusionsThe largest impacts on utility included three generic dimensions (i.e., pain, support, and work) and nausea, a symptom caused by cancer (e.g., brain tumours, gastrointestinal tumours, malignant bowel obstruction) and by common treatments (e.g., chemotherapy, radiotherapy, opioid analgesics). This may make the FACT-8D more informative for CUA evaluating in many cancer contexts, an assertion that must now be tested empirically in head-to-head comparisons with generic utility measures.